# Hausman test for panel data

I am performing a Hausman test to decide whether to use fixed effects or random effects model. The results I get are as follows:

. hausman random fixed

---- Coefficients ----
|      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
|     random       fixed        Difference          S.E.
-------------+----------------------------------------------------------------
opm |    .0375723     .0128309        .0247414        .0029346
tadiv10m |    .0000558     .0000532        2.67e-06        .0000101
auditcomm |    .0765687     .0572845        .0192842        .0087329
nplsgrossl~n |    .2700572     .0569666        .2130906        .0193822
govauditor |   -.0628177     -.040186       -.0226318        .0042376
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test:  Ho:  difference in coefficients not systematic

chi2(5) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=      341.23
Prob>chi2 =      0.0000


and

. hausman fixed ., sigmamore

Note: the rank of the differenced variance matrix (4) does not equal the number of coefficients being tested (5);
be sure this is what you expect, or there may be problems computing the test.  Examine the output of your
estimators for anything unexpected and possibly consider scaling your variables so that the coefficients
are on a similar scale.

---- Coefficients ----
|      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
|     fixed          .          Difference          S.E.
-------------+----------------------------------------------------------------
opm |    .0128309     .0375723       -.0247414        .0010828
tadiv10m |    .0000532     .0000558       -2.67e-06        4.60e-07
auditcomm |    .0572845     .0765687       -.0192842        .0008345
nplsgrossl~n |    .0569666     .2700572       -.2130906        .0091677
govauditor |    -.040186    -.0628177        .0226318        .0010184
------------------------------------------------------------------------------
b = consistent under Ho and Ha; obtained from xtreg
B = inconsistent under Ha, efficient under Ho; obtained from xtreg

Test:  Ho:  difference in coefficients not systematic

chi2(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=      621.45
Prob>chi2 =      0.0000


How do I go about interpreting the results?

• Explaining the software you used is always helpful to somebody who doesn't recognise what it is. Here it's Stata. It's irrelevant to the question, but others might be interested in related questions for which it is relevant. – Nick Cox Mar 2 '15 at 14:12

What you are looking for is the $\chi^2$ statistic produced at the end of the test. The null hypothesis of the Hausman test is that the fixed and random effects model do not differ significantly from each other. A significant test statistic means that we reject the null.

    Test:  Ho:  difference in coefficients not systematic

the value of the test statistic is 341.23 and the p-value shows that this value is significant at the 1% level and even below (Prob>chi2 = 0.0000).